Mechanism and Direct Kinetic Study of the Polychlorinated Dibenzo-p

Dec 13, 2010 - A direct density functional theory (DFT) kinetic calculation is carried out for the homogeneous gas-phase formation of polychlorinated ...
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Environ. Sci. Technol. 2011, 45, 643–650

Mechanism and Direct Kinetic Study of the Polychlorinated Dibenzo-p-dioxin and Dibenzofuran Formations from the Radical/Radical Cross-Condensation of 2,4-Dichlorophenoxy with 2-Chlorophenoxy and 2,4,6-Trichlorophenoxy FEI XU, WANNI YU, QIN ZHOU, RUI GAO, XIAOYAN SUN, QINGZHU ZHANG,* AND WENXING WANG Environment Research Institute, Shandong University, Jinan 250100, People’s Republic of China

Received August 5, 2010. Revised manuscript received November 27, 2010. Accepted November 29, 2010.

A direct density functional theory (DFT) kinetic calculation is carried out for the homogeneous gas-phase formation of polychlorinated dibenzo-p-dioxins and dibenzofurans (PCDD/ Fs) from the cross-condensation of 2,4-dichlorophenoxy radical (2,4-DCPR) with 2-chlorophenoxy radical (2-CPR) and 2,4,6trichlorophenoxy radical (2,4,6-TCPR). The possible formation mechanism is investigated and compared with the PCDD/F formation mechanism from the self-condensation of 2,4-DCPR, 2-CPR, and 2,4,6-TCPR. The rate constants and their temperature dependence of the crucial elementary reactions are computed by the canonical variational transition-state theory with the small curvature tunneling contribution over the temperature range of 600-1200 K. This study shows that the multichlorine substitutions suppress the PCDD/F formations. Because of a lack of experimental kinetic data, the present theoretical results are expected to be useful and reasonable to estimate the kinetic properties, such as the pre-exponential factors, the activation energies, and the rate constants, of the elementary reactions involved in the formation of PCDD/Fs.

1. Introduction Incineration as a municipal solid waste management strategy has a number of advantages, namely, reduction of volume and weight and reuse of the energy in the waste. Major disadvantages of incineration processes are, however, the emissions of toxic chlorinated aromatic compounds, such as dioxinssthe class of polychlorinated dibenzo-p-dioxin (PCDDs) and polychlorinated dibenzofurans (PCDFs). Dioxins are notorious for their biochemical and toxic effects (1-3). PCDD/PCDF (PCDD/F for short) emissions from municipal waste incinerators (MWIs) have raised serious concerns globally and led to severe difficulties in constructing both municipal and hazardous waste incinerators (4, 5). A * Corresponding author e-mail: [email protected]; fax: 86-531-8836 1990; phone: 86-531-8836 9788. 10.1021/es102660j

 2011 American Chemical Society

Published on Web 12/13/2010

mechanistic understanding of the formation of PCDD/Fs is of practical value as well as fundamental interest. PCDD/F formation rates from precursors that are similar in structure, such as chlorophenols (CPs), have been found to be significantly faster than rates from particulate carbon, or de novo synthesis, under typical incinerator conditions (6-8). Also, it is well-known that CPs are among the most abundant aromatic compounds found in MWI flue gases (8, 9). Precursor pathways from CPs are the most important for the formation of PCDD/F congeners. Considerable studies have been conducted on the PCDD/F formations from CPs under various experimental conditions (10-16). However, most of the research focused on the self-condensation of single CP precursors. The cross-condensation of different CP pairs is responsible for the distribution of PCDD/F homologues as well. For example, the most abundant P5CDD isomers, 1,2,4,6,8-P5CDD, 1,2,4,7,9-P5CDD, 1,2,3,6,8-P5CDD, and 1,2,3,7,9-P5CDD, are produced from the cross-condensation of 2,4,6-trichlorophenol (2,4,6-TCP) with 2,3,4,6tetrachlorophenol (2,3,4,6-TeCP) (17). In addition, the study of Ryu showed that PCDF isomers formed from CPs with different numbers of Cl atoms are favored over isomers formed from CPs with similar numbers of Cl atoms, due to steric effects associated with a parallel plane approach geometry of reacting phenoxy radicals (18). However, little attention has been given to the formation of PCDD/Fs from the cross-condensation of different CP pairs. Chlorophenoxy radicals (CPRs) have been identified as key intermediates in essentially all proposed pathways of the formation of PCDD/Fs. The radical/radical condensation of CPRs plays a crucial role in the dioxin formations, especially in the homogeneous gas-phase formation of PCDD/Fs (19, 20). The formation of CPRs from CPs, which is the initial step in the formation of PCDD/Fs, has been investigated in detail in the literature (21-23). Owing to their significant resonance stabilization, a considerable concentration of CPRs could build up in the combustion environment to enable condensation to occur. It is difficult to obtain experimental results related to the formation pathway of PCDD/Fs due to a lack of efficient detection schemes for radical intermediate species. Quantum chemical calculation is a widely adopted tool to find the favorite reaction pathways and reaction sites. Furthermore, several research studies pointed out that the scarceness of rate parameters for the elementary reactions involved in the formation of PCDD/Fs is the most difficult challenge in further improving PCDD/F formation models and suggested that additional attention be paid to estimating these parameters (18, 24-27). In this paper, therefore, we focus our interest on a quantum mechanical and direct kinetic study of the homogeneous gas-phase formation of PCDD/Fs from the radical/radical cross-condensation of 2,4-dichlorophenoxy radical (2,4-DCPR) with 2-chlorophenoxy radical (2CPR) and 2,4,6-trichlorophenoxy radical (2,4,6-TCPR). This work complements and expands our previously published studies on the PCDD/F formations from the self-condensation of 2,4-DCPR, 2-CPR, and 2,4,6-TCPR (28, 29).

2. Computational Methods All geometries are fully optimized at the MPWB1K/631+G(d,p) level of theory (30) using the Gaussian 03 suite of programs (31). For all stationary points, frequency calculations are performed to verify whether they are minima with all positive frequencies or transition states with only one imaginary frequency. The intrinsic reaction coordinate (IRC) calculations are carried out at the MPWB1K/6-31+G(d,p) VOL. 45, NO. 2, 2011 / ENVIRONMENTAL SCIENCE & TECHNOLOGY

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FIGURE 1. PCDD formation routes embedded with the potential barriers ∆E (kcal/mol) and reaction heats ∆H (kcal/mol) from the cross-condensation of 2,4-DCPR with 2-CPR. ∆H is calculated at 0 K.

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level to confirm that the transition state connects to the right minima along the reaction path. Moreover, the energies are further refined at the MPWB1K/6-311+G(3df,2p) level on the basis of the MPWB1K/6-31+G(d,p)-optimized geometries. To obtain the rate constants and activation energies, the POLYRATE 9.3 program (32) is employed with the aid of the canonical variational transition-state (CVT) theory (33-35) with the small curvature tunneling (SCT) contribution (36).

3. Results and Discussion The optimized geometries and the calculated vibrational frequencies of 2-CP and 2-monochlorodibenzo-p-dioxin (2MCDD) at the MPWB1K/6-31+G(d,p) level show good consistency with the corresponding experimental values, and the relative deviation remains within 1.0% for the geometrical parameters and 8.0% for the vibrational frequencies except for the largest frequency of 2-CP (its relative error is 11.4%). For the reaction of 2,4-DCP + 2-CP f 1,3-DCDD + H2 + HCl (DCDD ) dichlorodibenzo-p-dioxin), the reaction enthalpy calculated at the MPWB1K/6-311+G(3df,2p)//MPWB1K/631+G(d,p) level and at 298.15 K is 21.88 kcal/mol, which matches well with the corresponding value of 22.78 kcal/

mol derived from the measured standard enthalpies of formation (37-40). 3.1. PCDD Formations. 3.1.1. PCDD Formations from the Cross-Condensation of 2,4-DCPR with 2-CPR. Relatively more PCDD congeners can be formed from the crosscondensation of 2,4-DCPR with 2-CPR compared to those formed from the self-condensation of 2,4-DCPR as well as 2-CPR. For illustration, possible formation routes are displayed in Figure 1. As shown in Figure 1, all PCDD formation pathways start with oxygen-carbon coupling, followed by Cl or H abstraction. In pathways 1, 4, 5, 8, 9, 11, and 14, ring closure and intra-annular elimination of Cl occur in a onestep reaction and are the rate-determining step. Intra-annular elimination of H is the rate-determining step for pathways 2, 3, 6, 7, 10, 12, and 13 due to the high barrier and strong endothermicity. It is clear from Figure 1 that pathway 1 has relatively fewer elementary steps compared to pathways 2 and 3. In addition, the rate-determining step involved in pathway 1 requires a lower barrier and is less endoergic than those involved in pathways 2 and 3. Thus, pathway 1 is favored over pathways 2 and 3. Similarly, pathway 5 is favored over pathways 6 and 7, pathway 9 is favored over pathway 10, and pathway 11 is

FIGURE 2. PCDD formation routes embedded with the potential barriers ∆E (kcal/mol) and reaction heats ∆H (kcal/mol) from the cross-condensation of 2,4-DCPR with 2,4,6-TCPR. ∆H is calculated at 0 K. VOL. 45, NO. 2, 2011 / ENVIRONMENTAL SCIENCE & TECHNOLOGY

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FIGURE 3. 2,4,6-TCDF formation routes embedded with the potential barriers ∆E (kcal/mol) and reaction heats ∆H (kcal/mol) from the cross-condensation of 2,4-DCPR with 2-CPR. ∆H is calculated at 0 K. favored over pathways 12 and 13. Pathway 8 includes two more elementary steps than pathway 5. However, the ratedetermining step involved in pathway 5 has a higher barrier and is more endothermic compared to that involved in pathway 8. Therefore, pathways 5 and 8 should be competitive. For the same reason, pathways 1 and 4 should be competitive and pathways 11 and 14 should be competitive. Therefore, the thermodynamically favored PCDD formation pathways are pathways 1, 4, 5, 8, 9, 11, and 14. This reaffirms the previous conclusion that the thermodynamically favored PCDD formation pathways occur through intra-annular elimination of Cl (28). The resulting 2-MCDD, 1,3-DCDD, 646

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1,7-DCDD, and 1,8-DCDD are the dominant PCDD products from the cross-condensation of 2,4-DCPR with 2-CPR. 3.1.2. PCDD Formations from the Cross-Condensation of 2,4-DCPR with 2,4,6-TCPR. Figure 2 depicts the PCDD formation mechanism from the cross-condensation of 2,4DCPR with 2,4,6-TCPR. Similar to the cross-condensation of 2,4-DCPR with 2-CPR, all PCDD formation pathways start with oxygen-carbon coupling, followed by Cl or H abstraction. The oxygen-carbon coupling is a barrierless and strongly exothermic process. All of the Cl or H abstraction steps are highly exothermic. In pathways 15, 18, 19, 20, 21, and 22, ring closure and intra-annular elimination of Cl occur

FIGURE 4. 2,6-DCDF and 2,4-DCDF formation routes embedded with the potential barriers ∆E (kcal/mol) and reaction heats ∆H (kcal/mol) from the cross-condensation of 2,4-DCPR with 2-CPR. ∆H is calculated at 0 K.

FIGURE 5. PCDF formation route embedded with the potential barriers ∆E (kcal/mol) and reaction heats ∆H (kcal/mol) from the cross-condensation of 2,4-DCPR with 2,4,6-TCPR. ∆H is calculated at 0 K. in a one-step reaction and are the rate-determining step. Intra-annular elimination of H is the rate-determining step for pathways 16 and 17. As seen from Figure 2, PCDDs are preferentially formed from pathways 15, 18, 19, 20, 21, and 22, resulting in the formation of 1,3,7-TCDD, 1,3,8-TCDD, 1,3,6,8-TeCDD and 1,3,7,9-TeCDD (TCDD ) trichlorodibenzo-p-dioxin, and TeCDD ) tetrachlorodibenzo-p-dioxin), consistent with the study of Ryu (41). In general, 1,3,6,8-TeCDD and 1,3,7,9-TeCDD, the most abundant PCDD congeners found in municipal waste incinerators, are considered to be formed from the selfcondensation of 2,4,6-TCP. Comparison of the mechanism displayed in Figure 2 with a previous study (28) shows that the formation of 1,3,6,8-TeCDD and 1,3,7,9-TeCDD from the cross-condensation of 2,4-DCPR with 2,4,6-TCPR by one chlorine loss is favored over the formation of 1,3,6,8-TeCDD and 1,3,7,9-TeCDD from the self-condensation of 2,4,6-TCPR

by two chlorine losses. Moreover, the abundances of 2,4DCP and 2,4,6-TCP are almost equal in MWI flue gases. Therefore, the cross-condensation of 2,4-DCPR with 2,4,6TCPR should make a significant contribution to the distribution of 1,3,6,8-TeCDD and 1,3,7,9-TeCDD in MWIs. Comparison of the reaction pathways presented in Figures 1 and 2 with previous research (28, 29) clearly shows that the substitution pattern of chlorophenols has a significant influence on the PCDD formation mechanism, especially on the oxygen-carbon coupling of CPR. The exothermicities of the oxygen-carbon coupling for 2-CPR + 2-CPR, 2-CPR + 2,4-DCPR, 2,4-DCPR + 2,4-DCPR, 2,4-DCPR + 2,4,6-TCPR, and 2,4,6-TCPR + 2,4,6-TCPR are 23.04-24.50, 21.43-23.04, 20.26-21.14, 17.68-19.45, and 17.06 kcal/mol. The exothermicity of the oxygen-carbon coupling decreases with increasing number of chlorine substitutions. The ranking of the PCDD formation potential is as follows: 2-CPR + 2-CPR VOL. 45, NO. 2, 2011 / ENVIRONMENTAL SCIENCE & TECHNOLOGY

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TABLE 1. Arrhenius Formulasa for the Elementary Reactions Involved in the Thermodynamically Preferred Formation Pathways of PCDDs from the Cross-Condensation of 2,4-DCPR with 2-CPR and 2,4,6-TCPR over the Temperature Range of 600-1200 K reaction IM1 + H f IM5 + HCl IM1 + OH f IM5 + HOCl IM5 f 2-MCDD + Cl IM5 f IM7 IM7 f IM10 IM10 f 2-MCDD + Cl IM2 + H f IM11 + H2 IM11 f 1,3-DCDD + Cl IM11 f IM13 IM13 f IM16 IM16 f 1,3-DCDD + Cl IM3 + H f IM17 + HCl IM3 + OH f IM17 + HOCl IM17 f 2-MCDD + Cl IM4 + H f IM19 + H2 IM19 f 1,8-DCDD + Cl IM19 f IM21 IM21 f IM24 IM24 f 1,7-DCDD + Cl IM25 + H f IM28 + HCl IM25 + OH f IM28 + HOCl IM28 f 1,3,8-TCDD + Cl IM28 f IM30 IM30 f IM33 IM33 f 1,3,7-TCDD + Cl IM26 + H f IM34 + HCl IM26 + OH f IM34 + HOCl IM26 + Cl f IM34 + Cl2 IM34 f 1,3,8-TCDD + Cl IM34 f IM35 IM35 f IM36 IM36 f 1,3,7-TCDD + Cl IM27 + H f IM37 + H2 IM37 f 1,3,6,8-TeCDD + Cl IM37 f IM38 IM38 f IM39 IM39 f 1,3,7,9-TeCDD + Cl a

Arrhenius formula k(T) k(T) k(T) k(T) k(T) k(T) k(T) k(T) k(T) k(T) k(T) k(T) k(T) k(T) k(T) k(T) k(T) k(T) k(T) k(T) k(T) k(T) k(T) k(T) k(T) k(T) k(T) k(T) k(T) k(T) k(T) k(T) k(T) k(T) k(T) k(T) k(T)

) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )

(3.98 (2.02 (3.38 (1.37 (9.23 (7.67 (1.06 (2.55 (5.94 (4.01 (5.18 (1.89 (1.09 (2.54 (1.57 (2.52 (3.60 (1.04 (9.48 (5.51 (6.43 (5.28 (1.26 (3.25 (5.02 (3.84 (1.18 (5.02 (1.55 (1.83 (1.87 (3.50 (5.71 (5.52 (3.07 (1.70 (5.25

× × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × ×

10-11) exp(-3424.8/T) 10-11) exp(-6931.5/T) 1011) exp(-13833.2/T) 1012) exp(-12584.0/T) 1012) exp(-6968.1/T) 1011) exp(-12836.3/T) 10-11) exp(-2663.5/T) 1011) exp(-13936.9/T) 1011) exp(-11789.7/T) 1013) exp(-8721.6/T) 1011) exp(-12620.1/T) 10-11) exp(-3359.7/T) 10-11) exp(-7442.4/T) 1011) exp(-13578.8/T) 10-11) exp(-2198.1/T) 1011) exp(-13832.6/T) 1011) exp(-11373.4/T) 1013) exp(-7680.4/T) 1011) exp(-12786.6/T) 10-11) exp(-3723.3/T) 10-12) exp(-6453.2/T) 1011) exp(-14332.4/T) 1012) exp(-11828.3/T) 1011) exp(-4806.5/T) 1011) exp(-13802.3/T) 10-11) exp(-3976.2/T) 10-11) exp(-6457.9/T) 10-11) exp(-1630.7/T) 1012) exp(-14918.6/T) 1012) exp(-11452.0/T) 1013) exp(-8305.6/T) 1011) exp(-13975.9/T) 10-11) exp(-3486.3/T) 1010) exp(-12386.7/T) 1012) exp(-9365.3/T) 1013) exp(-8569.5/T) 1011) exp(-13581.6/T)

Units are s-1 and cm3 molecule-1 s-1 for unimolecular and bimolecular reactions.

TABLE 2. Arrhenius Formulasa for the Elementary Reactions Involved in the Formation of PCDFs from the Cross-Condensation of 2,4-DCPR with 2-CPR and 2,4,6-TCPR over the Temperature Range of 600-1200 K reaction IM40 IM41 IM42 IM43 IM40 IM44 IM45 IM46 IM40 IM47 IM47 IM48 IM48 IM48 IM49 IM50 IM51 IM52 IM52 IM52 IM53 IM54 IM55 IM56 IM56 IM56 IM59 a

648

+ H f IM41 + H2 f IM42 f IM43 f 2,4,6-TCDF + OH + H f IM44 + H2 f IM45 f IM46 f 2,4,6-TCDF + OH f IM47 + H f IM42 + H2 + H f IM45 + H2 + H f IM49 + HCl + OH f IM49 + HOCl + Cl f IM49 + Cl2 f IM50 f IM51 f 2,6-DCDF + OH + H f IM53 + HCl + OH f IM53 + HOCl + Cl f IM53 + Cl2 f IM54 f IM55 f 2,4-DCDF + OH + H f IM57 + HCl + OH f IM57 + HOCl + Cl f IM57 + Cl2 f 2,4,6,8-TeCDF + OH

Arrhenius formula k(T) k(T) k(T) k(T) k(T) k(T) k(T) k(T) k(T) k(T) k(T) k(T) k(T) k(T) k(T) k(T) k(T) k(T) k(T) k(T) k(T) k(T) k(T) k(T) k(T) k(T) k(T)

) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )

(2.62 (3.32 (1.77 (3.21 (2.65 (2.24 (1.79 (2.78 (1.34 (5.38 (3.84 (4.11 (1.16 (2.85 (3.65 (5.01 (2.83 (3.28 (2.01 (8.74 (1.32 (7.60 (3.49 (4.83 (1.34 (3.63 (3.17

Units are s-1 and cm3 molecule-1 s-1 for unimolecular and bimolecular reactions.

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× × × × × × × × × × × × × × × × × × × × × × × × × × ×

10-11) exp(-2999.8/T) 1012) exp(-9755.8/T) 1012) exp(-13710.2/T) 1013) exp(-10884.1/T) 10-11) exp(-3183.1/T) 1012) exp(-9338.0/T) 1012) exp(-14580.8/T) 1013) exp(-10216.7/T) 1012) exp(-5447.9/T) 10-13) exp(-7565.9/T) 10-13) exp(-7111.2/T) 10-11) exp(-3960.5/T) 10-12) exp(-7015.5/T) 10-11) exp(-3066.9/T) 1012) exp(-8966.3/T) 1012) exp(-15529.8/T) 1013) exp(-10275.9/T) 10-11) exp(-4080.9/T) 10-12) exp(-7495.6/T) 10-11) exp(-3228.8/T) 1012) exp(-8654.6/T) 1012) exp(-16507.9/T) 1013) exp(-9758.7/T) 10-11) exp(-3817.4/T) 10-12) exp(-6855.4/T) 10-11) exp(-2799.4/T) 1013) exp(-10982.1/T)

> 2-CPR + 2,4-DCPR > 2,4-DCPR + 2,4-DCPR > 2,4-DCPR + 2,4,6-TCPR > 2,4,6-TCPR + 2,4,6-TCPR. This means that the PCDD formations are favored from less chlorinated phenols. The result is supported by the experimental evidence that the PCDD yields and homologue fractions decrease with increasing number of chlorine substituents (17, 41). Although o-chlorine is needed for the formation of PCDDs (28), multichlorine substitutions suppress the PCDD formations. 3.2. Formation of PCDFs. Three PCDF congeners, 2,4,6TCDF, 2,6-DCDF, and 2,4-DCDF (TCDF ) trichlorodibenzofuran, DCDF ) dichlorodibenzofuran), can be formed from the cross-condensation of 2,4-DCPR with 2-CPR. Four possible formation pathways are depicted in Figure 3 to explain the formation of 2,4,6-TCDF. Pathways 23 and 24 are similar, and they involve five elementary steps: carbon-carbon coupling, H abstraction, tautomerization (H shift), ring closure, and elimination of OH. The ring closure process has a large barrier and is strongly endoergic, and it is the rate determining-step. Pathway 25 is similar to pathway 26, which also involves five elementary processes: carbon-carbon coupling, tautomerization (double H transfer), H abstraction, ring closure (the rate-determining step), and elimination of OH. Pathways 27 and 28 in Figure 4 illustrate 2,6-DCDF and 2,4-DCDF being formed from the cross-condensation of 2,4DCPR with 2-CPR. The intermediate IM40 can be regarded as a prestructure for 2,4,6-TCDF. IM48 is a prestructure of 2,6-DCDF, and IM52 is a prestructure of 2,4-DCDF. As seen from Figure 3, the formation of IM40 is more exothermic than the formations of IM48 and IM52. Furthermore, the rate-determining step involved in the formation of 2,4,6TCDF has a lower barrier and is less endothermic compared to those involved in the formation of 2,6-DCDF and 2,4DCDF. Thus, the formation of 2,4,6-TCDF is preferred over the formation of 2,6-DCDF and 2,4-DCDF. Due to the symmetry of 2,4,6-TCPR, only one possible PCDF formation pathway, displayed in Figure 5, is proposed for the crosscondensation of 2,4-DCPR with 2,4,6-TCPR. Comparison with the previous studies (28, 29) tells us that the PCDF formation mechanism is controlled largely by the substitution pattern of chlorophenols. Steric and electronic effects associated with chlorine substitution suppress the dimerization of CPR. The ranking of the PCDF formation potential is as follows: PhR + 2-CPR > 2-CPR + 2,4-DCPR > 2,4-DCPR + 2,4-DCPR > 2,4-DCPR + 2,4,6-TCPR. This is consistent with the experimental observation that the PCDF formations are favored from less chlorinated phenols (18, 41). 3.3. Rate Constant Calculations. On the basis of the MPWB1K/6-311+G(3df,2p)//MPWB1K/6-31+G(d,p) energies, canonical variational transition-state rate calculations augmented by the small curvature tunneling corrections (CVT/SCT) are carried out in the temperature range of 600-1200 K. Our recently published studies show that the CVT/SCT rate constants of C6H5OH + H f C6H5O + H2, C6H5OH + OH f C6H5O + H2O are in good agreement with the corresponding experimental values (21, 22). In particular, direct inspection of the transition-state low-frequency mode indicates that the modes of the lowest frequency involved in TS12, TS21, TS24, TS28, TS40, TS51, TS53, TS57, TS63, TS68, TS72, TS73, TS77, and TS83 are hindered internal rotation instead. These modes are removed from the vibration partition function for the transition state, and the corresponding hindered rotor partition function, QHR(T), calculated by the method devised by Truhlar (42), is included in the expression of the rate constant. To be used more effectively, the CVT/SCT rate constants are fitted, and Arrhenius formulas are given in Table 1 for the elementary reactions involved in the thermodynamically preferred formation pathways of PCDDs and in Table 2 for

the elementary reactions involved in the formation of PCDFs from the cross-condensation of 2,4-DCPR with 2-CPR and 2,4,6-TCPR.

Acknowledgments This work was supported by the National Natural Science Foundation of China (Project 20737001) and Shandong Province Outstanding Youth Natural Science Foundation (Project JQ200804). We thank Professor Donald G. Truhlar for providing the POLYRATE 9.3 program.

Supporting Information Available Total energies (au), zero-point energies (au), and imaginary frequencies (cm-1) for the transition states and geometries in terms of Cartesian coordinates (Å) for the reactants, products, intermediates, and transition states. This material is available free of charge via the Internet at http:// pubs.acs.org.

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